Exam (elaborations)
IIT JEE pyq with solutions
- Course
- Institution
Hello students !I will provide you pyq along with solutions of JEE main+advanced and school notes of 11th and alert and focused!
[Show more]
Seller
Follow
[deepyadav]1
Content preview
VECTOR ALGEBRAVECTOR ALGEBRA
1. Let aˆ, bˆ be unit vectors. If c be a vector such that the 6. Let a iˆ ˆj kˆ and c 2iˆ 3iˆ 2k . Then the
number of vectors b such that b c a and
angle between â and c is , and bˆ c 2 c aˆ ,
12
b 1, 2,........,10 is :
2
then 6c is equal to
(a) 0 (b) 1
(a) 6 3 3 (b) 3 3 (c) 2
(d) 3
7. Let a and b be the vectors along the diagonal of a
(c) 6 3 3 (d) 6 3 1 parallelogram having area 2 2. let the angle between
2. Let â and b̂ be two unit vectors such that
a and b be acute. a 1 and a b a b . If
aˆ bˆ 2 aˆ bˆ 2. If 0, is the angle
c 2 2 a b 2b , then the angle between b and c
between â and bˆ, then among the statements :
is :
S1 : 2 aˆ bˆ aˆ bˆ
(a) (b)
4 4
S 2 : The projection of
â on â bˆ is 1
2 (c)
5
(d)
3
(a) Only (S1) is true 6 4
(b) Only (S2) is true 8. Let a iˆ 2 ˆj kˆ and b 2iˆ ˆj kˆ, where
(c) Both (S1) and (S2) are true R. If the area of the parallelogram whose adjacent
(d) Both (S1) and (S2) are false
sides are represented by the vectors a and b is
3. Let a a1iˆ a2 ˆj a3 kˆ ai 0, i 1, 2,3 be a vector 2 2
which makes equal angles with the coordinates axes
15 2 4 , then the value of 2 a a b b is
OX , OY and OZ . Also, let the projection of a on the equal to
(a) 10 (b) 7
vector 3iˆ 4 ˆj be 7. Let b be a vector obtained by
(c) 9 (d) 14
rotating a with 90 . If a , b and x-axis are coplanar, 9.
Let a be a vector which is perpendicular to the vector
then projection of a vector b on 3iˆ 4 ˆj is equal to
3iˆ
1ˆ
2
j 2kˆ. If a 2iˆ kˆ 2iˆ 13 ˆj 4kˆ, then the
(a) 7 (b) 2
(c) 2 (d) 7 projection of the vector a on the vector 2iˆ 2 ˆj kˆ is
4. If a b 1, b 1, b c 2 and c a 3, then the value 1
(a) (b) 1
3
of a b c , b c a , c b a is :
5 7
(c) (d)
(a) 0 (b) 6a b c 3
3
10. Let a iˆ 3 ˆj kˆ, b 3iˆ ˆj 4k and
(c) 12c a b (d) 12b c a
ˆ
c i 2 ˆj 2k , , R , be three vectors. If the
5. Let a iˆ ˆj 2kˆ, b 2iˆ 3 ˆj kˆ are c iˆ ˆj k be
10
three given vectors. Let v be a vector in the plane of a projection of a on c is and
3
2
and b whose projection on c is . If v ˆj 7, then b c 6iˆ 10 ˆj 7 kˆ, then the value of equal
3
to :
ˆ ˆ
v i k is equal to (a) 3 (b) 4
(a) 6 (b) 7 (c) 5 (d) 6
(c) 8 (d) 9 11. Let A, B, C be three points whose position vectors
respectively are :
, VECTOR ALGEBRA
a iˆ 4 ˆj 3kˆ 4 5
(c) (d)
5 6
b 2iˆ ˆj 4kˆ, R
16. Let a iˆ ˆj kˆand b 3i 5 ˆj 4kˆ be two
ˆ
c 3iˆ 2 ˆj 5kˆ
vectors, such that a b iˆ 9iˆ 12kˆ. Then the
If is the smallest positive integer for which a, b , c
projection of b 2a on b a is equal to
ar e non-collinear, then the length of the median, in
ABC , through A is : 39
(a) 2 (b)
5
82 62
(a) (b) 46
2 2 (c) 9 (d)
5
69 66
(c) (d) 17. Let a 2iˆ ˆj 5kˆ and b iˆ ˆj 2kˆ. If
2 2
23
12. Let ABC be
a triangle
such that
a b iˆ kˆ , then b 2 ˆj is equal to
2
BC a , CA b , AB c , a 6 2, b 6 3, and
(a) 4 (b) 5
b c 12 consider the statements : (c) 21 (d) 17
S1 : a b c b c 6 2 2 1
18. Let vector a has a magnitude 9. Let a vector b be
such that for every x, y R R 0, 0 , the vector
2
S 2 : ABC cos . Then
1
3
xa yb is perpendicular to the vector 6 ya 18 xb .
(a) Both (S1) and (S2) are true
Then the value of a b is equal to :
(b) Only (S1) is true
(c) Only (S2) is true (a) 9 3 (b) 27 3
(d) Both (S1) and (S2) are false (c) 9 (d) 81
13. Let a iˆ ˆj 2kˆ and b be a vector such that 19. Let S be the set of all a R for which the angle
between the vectors u a log e b iˆ 6 j 3kˆ and
a b 2iˆ kˆ and a b 3. Then the projection of b
on the vector a b is :- v log e b iˆ 2 j 2a log e b kˆ, b 1 is acute.
2 3 Then S is equal to:
(a) (b) 2
21 7 4
(a) – , (b)
2 7 2 3
(c) (d)
3 3 3 4 12
(c) , 0 (d) ,
14. Let a iˆ ˆj k and b 2iˆ ˆj kˆ, and 0. If
ˆ 3 7
the projection of a b on the vector i 2 ˆj 2kˆ is 20. Let a 3iˆ ˆj and b iˆ 2 ˆj kˆ. Let c be a vector
30, then is equal to
satisfying a b c b c. If b c are non-parallel,
15 then the value of is:
(a) (b) 8
2 (a) 5 (b) 5
13 (c) 1 (d) –1
(c) (d) 7
2 21. Let â and b̂ be two unit vectors such that the angle
15. A vector a is parallel to the line of intersection of the
between them is . If is the angle between the
plane determined by the vectors iˆ, iˆ ˆj and the plane 4
determined by the vectors iˆ ˆj , iˆ kˆ. The obtuse
vectors â bˆ
and aˆ 2bˆ 22 aˆ bˆ , then the
angle between a and the vector b iˆ 2 ˆj 2kˆ is value of 164 cos 2 is equal to :
3 2 (a) 90 27 2 (b) 45 18 2
(a) (b)
4 3
(c) 90 3 2 (d) 54 90 2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller [deepyadav]1. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
77254 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now